Vibration-based damage detection techniques have gained popularity in structural health monitoring due to their non-destructive nature. Most of such damage detection techniques on buildings have developed considering fixed base foundation, that is without considering effect of soil underneath. The objective of the present study is to develop a closed-form expression for determining damage severity in a shear building considering flexible boundary condition that is soil-structure interaction (SSI) using frequency response function (FRF)-based approach. The main concern is to understand the influence of SSI on structural damage quantification during post-seismic mitigation through numerical as well as experimental study. A numerical simulation has been performed on a 14-storey shear building with various soil conditions, namely fixed, dense, medium and soft soil. In the experimental investigation, the dimensions of the soil mass have been considered in such a way that free-field response can be replicated. By similitude laws, a geometric scale factor has been applied to develop a small-scale model and an equivalent shear beam (ESB) container. Damage severity has been determined for both numerical and experimental studies. The effectiveness of the proposed approach has been further studied for a real structure. The novelty of the study lies in the mathematical development involving minimum number of sensors as well as in modelling the effect of semi-infinite soil layer under a scaled-down model. The proposed approach is effective in identifying intermediate and ground storey damage. However, further investigation is required for quantifying complex damage patterns.

In this paper, closed-form expressions to calculate both the mean annual failure rate and the confidence factor are proposed. Reliability indicators are estimated assuming a normalization between capacity and demand called IDC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I_{DC}$$\end{document}. Simplified closed-form expressions are obtained in accordance with the probability seismic demand analysis used in SAC/FEMA. Uncertainties associated to mechanical, geometrical, and epistemic properties are taken into account, as well as uncertainties related to the occurrence of earthquakes. A comparison of both the mean annual failure rate and the confidence factor with IDC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I_{DC}$$\end{document} and the expressions proposed by Cornell and collaborators is performed. The numerical approach for the mean annual failure rate is obtained to verify the approximation of the closed-form solutions. Reliability indicators are obtained using six continuous reinforced concrete bridges designed to comply with three drift thresholds (0.002, 0.003 and 0.004). The bridge systems are situated in transition soil of Mexico City. Maximum differences of 4.1% and 10.6% are obtained between the proposed expression and the numerical solution for the mean annual rate of failure, estimated for two limit states: serviceability and collapse. The confidence factor presents differences of 5.2% between the present study and the original formulation.